Outliers

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#13985

Outliers

An outlier is a score that is unusual, or different from the bulk of the scores. A score is an outlier if it is more than 1.5 times the IQR (interquartile range) below Q₁ or more than 1.5 times the IRQ above Q_3.

Q₁ – 1.5 × IQR
Q₃ + 1.5 × IQR

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#18619

A set of data has a lower quartile of 22 and an upper quartile of 27. Which of the following values could be an outlier?

a. 15   b. 22    c.  24.5    d. 29     e.  35

IQR = 27 – 22

= 5

lower limit = 22 – 1.5 × 5

= 14.5

upper limit = 22 + 1.5 × 5

= 29.5

E is outlier as it is higher than the upper limit of 29.5

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#18620

Joe created a box and whisker plot from collected data. He claimed that the lowest score must be an outlier. Is he correct? Justify your answer with appropriate calculations.
IQR = Q3 – Q1 = 60 – 45 = 15	Find the IQR (interquartile range) IQR = Q3 – Q1  20 is the minimum 45 is Q1 55 is the median 60 is Q3 70 is the maximum
45 – 1.5 × 15 = 22.5	test if outlier using formula Q1 – 1.5 × IQR
since the lowest score is 20, which is below the cut off point of 22.5, then yes, the lowest score is considered to be an outlier, so Joe is correct	any score lower than this is considered an outlier

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#18622

Seeds were planted in a controlled environment. The heights of the resulting plants were recorded some weeks later. The data collected was found to have an interquartile range of 12cm with a lower quartile of 22cm.  Which of the following plant heights would be considered an outlier of the data collected? a. 3cm b. 4cm c. 35cm d. 50cm
22 – 1.5 × 12 = 4	IQR = 12cm Q1 = 22cm test if outlier using formula Q1 – 1.5 × IQR
∴ A	any score lower than 4 is an outlier

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